In: Economics
(a) Lower interest rate in US will decrease foreign investment in US, increasing net capital outflow, which will decrease the demand for dollar, depreciating the dollar. This will make US exportable goods more competitive and imported goods costlier, increasing exports and decreasing imports, which will increase net exports, therefore increasing trade balance (reducing trade deficit, or increasing trade surplus).
(b) If Japanese citizens divest US stock market, increasing net capital outflow, which will decrease the demand for dollar, depreciating the dollar. This will make US exportable goods more competitive and imported goods costlier, increasing exports and decreasing imports, which will increase net exports, therefore increasing trade balance (reducing trade deficit, or increasing trade surplus).
(c) If income in US increases, aggregate demand rises faster than increase in aggregate supply, so import demand rises. Ceteris paribus, increase in import demand will decrease net exports, which will reduce the trade balance (increasing trade deficit, or decreasing trade surplus).